EduSahara™ Worksheet

Question 1

1.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?

(i)

∠e
(ii)

∠d
(iii)

∠b
(iv)

∠c

Question 2

2.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
60°
.
If the height of the
radio tower
is
40 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

40
3

√

18

m
(ii)

40
3

√

3

m
(iii)

20

√

2

m
(iv)

40

m
(v)

40
3

m

Question 3

3.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° with the ground. The top of the tree touches the ground at a distance of 60 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

223.93 m
(ii)

240.93 m
(iii)

207.93 m
(iv)

239.93 m
(v)

220.93 m

Question 4

4.

A flagstaff stands on the top of a building at a distance of 15 m away from the foot of building . The angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 45°. Find the height of the flagstaff .

(i)

(

15

√

18

−

15

√

6

)

m
(ii)

450

m
(iii)

(

15

√

3

−

15

)

m
(iv)

(

45
2

√

2

−

15
2

√

6

)

m
(v)

(

2

−

√

3

)

m

Question 5

5.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 70 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the width of the river .

(i)

73.00 m
(ii)

67.00 m
(iii)

75.00 m
(iv)

65.00 m
(v)

70.00 m

Question 6

6.

The angles of depression of two boats from the top of a cliff 90 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

68.89 m
(ii)

60.89 m
(iii)

65.89 m
(iv)

70.89 m
(v)

62.89 m

Question 7

7.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?

(i)

∠c
(ii)

∠e
(iii)

∠d
(iv)

∠f

Question 8

8.

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 20 min for the angle of depression to change from 30° to 60°, how soon after this, will the car reach the observation tower?

(i)

12 min 7 sec
(ii)

10 min 0 sec
(iii)

8 min 2 sec
(iv)

11 min 6 sec
(v)

9 min 4 sec

Question 9

9.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
45°
.
If the distance between the point and the top of the
building
is
110 m
,
find the distance between
the observation point and the foot of the
building
.

(i)

55

√

2

m
(ii)

55

m
(iii)

110

m
(iv)

110

√

3

m
(v)

55
2

√

12

m

Question 10

10.

A person, walking 15 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 45°. Find the height of the flagpost .

(i)

(

2

+

√

3

)

m
(ii)

(

15
2

√

3

+

15
2

)

m
(iii)

(

45
4

√

2

+

15
4

√

6

)

m
(iv)

(

15
2

√

18

+

15
2

√

6

)

m
(v)

225
2

m

Question 11

11.

A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 60° and 30° and the distance between them is 130 m , find the height of the cliff.

(i)

53.30 m
(ii)

59.30 m
(iii)

61.30 m
(iv)

56.30 m
(v)

51.30 m

Question 12

12.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 30°. If the height of the building is 16 m, find the height of the flag staff .

(i)

37.00 m
(ii)

27.00 m
(iii)

32.00 m
(iv)

29.00 m
(v)

35.00 m

Question 13

13.

From a point 200 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 45° and 30° respectively. Find the height of the cliff.

(i)

98.48 m
(ii)

100.48 m
(iii)

133.48 m
(iv)

142.48 m
(v)

115.48 m

Question 14

14.

Two boys are on opposite sides of a tower of 50 m height. They measure the angle of elevation of the top of the tower as 45° and 30° respectively. Find the distance between the two boys.

(i)

(

−

2

−

√

3

)

m
(ii)

(

25

√

6

+

75

√

2

)

m
(iii)

(

50

√

6

+

50

√

18

)

m
(iv)

(

−

5000

)

m
(v)

(

50

+

50

√

3

)

m

Question 15

15.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
60°
.
If the distance between the point and the top of the
building
is
40 m
,
find the height of the
building
.

(i)

20

m
(ii)

20

√

3

m
(iii)

20

√

18

m
(iv)

60

m
(v)

30

√

2

m

Question 16

16.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
45°
.
If the distance between the point and the foot of the
radio tower
is
190 m
,
find the height of the
radio tower
.

(i)

193

m
(ii)

187

m
(iii)

190

m
(iv)

191

m
(v)

189

m

Question 17

17.

The angles of depression of two boats from the top of a cliff 180 m high are 60° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

387.71 m
(ii)

437.71 m
(iii)

411.71 m
(iv)

415.71 m
(v)

422.71 m

Question 18

18.

Two vertical poles are on either side of a road. A 33 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 30° with the pole and when it is turned to rest against another pole, it makes an angle of 60° with the road. Find the width of the road.

(i)

48.08 m
(ii)

42.08 m
(iii)

45.08 m
(iv)

40.08 m
(v)

50.08 m

Question 19

19.

From a point 90 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 30° respectively. Find the height of the pillar.

(i)

80.92 m
(ii)

111.92 m
(iii)

103.92 m
(iv)

128.92 m
(v)

100.92 m

Question 20

20.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 45° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 17 m, find the height of the building .

(i)

26.23 m
(ii)

23.23 m
(iii)

18.23 m
(iv)

20.23 m
(v)

28.23 m

Question 21

21.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 180 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the height of the other temple.

(i)

122.00 m
(ii)

120.00 m
(iii)

138.00 m
(iv)

117.00 m
(v)

97.00 m

Question 22

22.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
30°
.
If the distance between the point and the foot of the
radio tower
is
50 m
,
find the distance between
the observation point and the top of the
radio tower
.

(i)

100
3

√

18

m
(ii)

100

m
(iii)

50

√

2

m
(iv)

100
3

m
(v)

100
3

√

3

m

Question 23

23.

The shadow of a vertical tower BA on a level ground is increased by 10 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .

(i)

23.66 m
(ii)

20.66 m
(iii)

28.66 m
(iv)

26.66 m
(v)

18.66 m

Question 24

24.

The angle of elevation of the top of a building from the foot of a tower is 45°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 30 m, find the height of the building .

(i)

17.32 m
(ii)

22.32 m
(iii)

12.32 m
(iv)

14.32 m
(v)

20.32 m

Question 25

25.

A
tower
stands vertically on the ground.

The height of the
tower
is
10

√

3

m
.

The distance between the observation point and its foot
is
10

m
.

Find the angle of elevation.

(i)

60°
(ii)

105°
(iii)

45°
(iv)

90°
(v)

30°

Assignment Key